Hi!
Thank you so much for this question! Self-employment taxes are confusing and especially when you are just getting your business going. The IRS (and states too if you live in a state with income taxes) require quarterly payments of taxes estimated to be owed. The concept is really the same for employees, except the employer withholds estimated taxes for you and sends them to the IRS or the state on your behalf.
If you are just switching over from having some wages to all self-employment, you need to consider if you have net income from your self-employment. I suggest you use TaxCaster (https://turbotax.intuit.com/tax-tools/calculators/taxcaster/) and enter as much information as possible, both your jobs and self-employment. This will assist you with knowing If you are going to owe at the end of the year and what you might need to pay for estimates, if at all.
